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Choose the correct option for (f:\mathbb{R}\to \mathbb{R}), (f(x)=\ln(1+x^2)).फलन (f:\mathbb{R}\to \mathbb{R}), (f(x)=\ln(1+x^2)) के लिए सही विकल्प चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not onto because negative values are not obtainedआच्छादक नहीं है क्योंकि ऋणात्मक मान नहीं मिलते
Step 1: Since (1+x^2\ge 1), (\ln(1+x^2)\ge 0). Step 2: The codomain (\mathbb{R}) contains negative values that are not obtained. Step 3: For logarithmic functions, check both the input expression and the minimum value.चरण 1: (1+x^2\ge 1) इसलिए (\ln(1+x^2)\ge 0)। चरण 2: सहक्षेत्र (\mathbb{R}) में ऋणात्मक मान हैं जो नहीं मिलते। चरण 3: लघुगणक वाले फलन में अंदर की मात्रा और न्यूनतम मान दोनों देखें।
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